Find vertex of f(x)=x^2+6x+10

The function f(x) = 6x + 8 is transformed to function g through a horizontal stretch by a factor of 5. What is the equation of f

elixir [45]

Answer:

$g(x) = 30\cdot x +40$ ; $a \approx 1.898$ , $k = 40$ .

Step-by-step explanation:

The resultant function is obtained by multiplying $f(x)$ by a real number $k$ . That is:

$g(x) = k \cdot f (x)$

If $k = 5$ and $f(x) = 6\cdot x + 8$ , then $g(x)$ is:

$g(x) = 5\cdot (6\cdot x + 8)$

$g(x) = 30\cdot x +40$

Given that presence of the expression $g(x) = 6^{a}\cdot x + k$ , then:

$6^{a} = 30$ and $k = 40$

The value of a is obtained by applying the definition of logarithms:

$a = \log_{6}30$

$a \approx 1.898$

Finally, the value of k is found by direct comparison:

$k = 40$

6 0

3 years ago

5. The width of a row of identical townhouses,

Serjik [45]

Answer:

a. The value of the constant k is 21

b. The equation is y = k * x, where k is the proportionality constant, "x" is the number of terraced houses and "y" is the width of a row of identical houses.

Step-by-step explanation:

a.

A proportional relationship satisfies the equation y = k * x, where k is a positive constant and is called a proportionality constant. In this case "x" is the number of terraced houses and "y" is the width of a row of identical houses.

The data you have is that the width of 5 townhouses are 105 feet. This means that the value of "x" is 5 houses and the value of "y" is 105 feet. By replacing in the equation y = k * x and isolating the constant k, you get:

105=k*5

$k=\frac{105}{5}$

k=21

So the value of the constant k is 21.

b.

As mentioned, the equation is y = k * x, where k is the proportionality constant, "x" is the number of terraced houses and "y" is the width of a row of identical houses.

This means that just as "x" increases, "y" increases. And that if "x" decreases, "y" will decrease. And this relationship between "x" e "and" will always be the same, determined by the value of the constant "k".

7 0

3 years ago

A streaming music site changed its format to focus on previously unreleased music from rising artists. The site manager now want

nika2105 [10]

Answer:

D) The manager should fail to reject the null hypothesis; there is not enough evidence to conclude that the number of unique daily listeners has changed.

Step-by-step explanation:

The scenario indicates the null hypotheses and alternative hypotheses are

Null hypotheses: The number of unique daily listeners hasn't changed.

Alternative hypotheses: The number of unique daily listeners has changed.

The null hypothesis is rejected if the calculated p-value is less significance level.

We are given that p-value is 0.0743 and confidence level=0.95.

Significance level =α=1-0.95=0.05.

As we can see the p-value is greater than significance level, so, we fail to reject the null hypotheses at 5% significance level.

Thus, we conclude at the 95% confidence level that the manager should fail to reject the null hypothesis; there is not enough evidence to conclude that the number of unique daily listeners has changed

8 0

3 years ago

Need help with a math question

Svetach [21]

Answer:

(x+1)^2+(y-7)^2=8

Step-by-step explanation:

You should try the next one and I can check work or tell you if it is right.

The diameter length can be found be computing the distance that (-3,5) is to (1,9) which is sqrt(4^2+4^2)=sqrt(32).

The radius is half the diameter so it is sqrt(32)/2.

The center of the circle is the midpoint of a diameter. So compute the (Average of x, average of y)=(-1,7)

So plug into (x-h)^2+(y-k)^2=r^2 we get

(x+1)^2+(y-7)^2=32/4

simplifying gives

(x+1)^2+(y-7)^2=8

(I had to type this twice; my cat jump on my keyboard)

4 0

3 years ago

Read 2 more answers

There are 20 machines in a factory. 7 of the machines are defective.

adelina 88 [10]

Answer:

0.1225

Step-by-step explanation:

Given

Number of Machines = 20

Defective Machines = 7

Required

Probability that two selected (with replacement) are defective.

The first step is to define an event that a machine will be defective.

Let M represent the selected machine sis defective.

P(M) = 7/20

Provided that the two selected machines are replaced;

The probability is calculated as thus

P(Both) = P(First Defect) * P(Second Defect)

From tge question, we understand that each selection is replaced before another selection is made.

This means that the probability of first selection and the probability of second selection are independent.

And as such;

P(First Defect) = P (Second Defect) = P(M) = 7/20

So;

P(Both) = P(First Defect) * P(Second Defect)

PBoth) = 7/20 * 7/20

P(Both) = 49/400

P(Both) = 0.1225

Hence, the probability that both choices will be defective machines is 0.1225

4 0

3 years ago